+1 on Ikea kitchens - I’ve assembled the stuff that’s in our back kitchen. Cheap and cheerful if that’s what you want and it’s wickedly easy - and very satisfying - to build.
I’d advise spending what you can afford on your kitchen appliances and furniture if you spend a lot of time there. It’s the centre of everything and you don’t want to be looking at stuff that annoys you, doesn’t work or doesn’t age well. We still have no floor on our sitting room but did invest in a decent kitchen that will age with us and outlast us. A word of warning if you go for solid wood worktops. Ours weren’t sealed properly - waxed, not oiled and it broke my heart. It took a lot of work (thanks to the advice of a pinster) to get them to where they should have been when we bought them. But I did the same as Slasher’s cousin and designed the kitchen myself based on what I need - I’m short, wanted no top cupboards, that kind of thing, and got lots of ideas from good magazines (which you can read for nothing in your library). It’s a brilliant room, it works and it’s warm and welcoming too. I’m not wildly houseproud in general and could care less about a lot of what’s involved, but the kitchen is magic.
Your work triangle is important. You should ideally be able to step or turn between your sink, fridge and cooker. Our cooker is in the island (don’t forget you’ll want sockets in your island, whether it holds a sink or cooker). If you’re short, a deep sink is great, and you should have the level of the worktops at a comfortable height for the person who’ll be working in it most.
Slasher is right re white sink to a point - but any sink will only look good if you’re cleaning it half a dozen times a day and in real life, who has time for that? Or the interest, but that’s life. Worse is that there’s no forgiveness if you drop things in a ceramic sink. They’re gone.
Invest in the best cooker/hob and dishwasher you can afford, because you’ll use them all the time and if they give trouble you’ll be heart-scalded. The fridge is less important by far.